Solve the equation on the interval [0, 2π).

Question

tan2x sin x = tan2x

would it be 0, pi/2 ?

Answer 1

well, you must have

tan2x = 0
or sinx = 1

so, you are almost right. tan2x=0 if 2x = 0 or π or 2π or 3π
so, x = 0, π/2, π, 3π/2
sinx = 1 if x = π/2, so that does not add any solutions to the list.